If the resultant torque of the system is zero, the angular momentum is conserved.

When the Lagrange function of motion does not explicitly contain a generalized coordinate, the generalized momentum of the corresponding coordinate is conserved.

When the Lagrangian function of motion does not explicitly include time, generalized energy is conserved.

For a fixed particle, as long as the velocity changes, the kinetic energy changes.

For a particle system, it depends on the total kinetic energy of the system. You'd better calculate whether its kinetic energy has changed according to the conservation of energy.

For rigid bodies, kinetic energy = translational kinetic energy+rotational kinetic energy.

I hope it will help you, and hope to adopt it.